# algebras set of numbers and formula

May 28th, 2015
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Definitions: N: Natural numbers N0: Whole numbers Z: Integers Z+: Positive integers Z-: Negative integers Q: Rational numbers I : Irrational numbers C: Complex numbers

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Algebra formulasSets of NumbersDefinitions:N: Natural numbers N0: Whole numbers Z: Integers Z+: Positive integers Z-: Negative integers Q: Rational numbers I : Irrational numbers C: Complex numbers Formulas: 1) Natural numbers (counting numbers ) 2) Whole numbers ( counting numbers with zero ) 3) Integers ( whole numbers and their opposites and zero ) 4) Rational numbers: repeating and terminating decimalsConverting repeating decimals to fractionsa=0.3333.... eqn(i)multiply both sides by 1010a=3.333..... eqn(ii)Subtract eqn (i) from eqn (ii) 10a=3.333.....- (a=0.3333......)____________________9a = 3.000....a=1/35) Rational numbers: non-repeating non-terminating decimals6) Real numbers: Union of rational and irrational numbers 7) Complex numbers: Complex numbersDefinitions:A complex number is written as a + bi where a and b are real numbers an i, called the imaginary unit, has the property that i2 = -1. The complex numbers a + bi and a - bi are called complex conjugate of each other. Formulas: 1) Equality of complex numbers a + bi = c + di if and only if a = c and b = d 2) Addition of complex numbers (a + bi) + (c + di) = (a + c) + (b + d)i 3) Subtraction of complex numbers (a + bi) - (c + di) = (a - c) + (b - d)i 4) Multiplication of complex numbers (a + bi)(c + di) = (ac - bd) + (ad + bc)i 5) Division of complex numbers 6) Polar form of complex numbers 7) Multiplication and division of complex numbers in pol

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